%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN134-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:26:54 PM UTC 2026
% Result : Unsatisfiable 2.03s 0.88s
% Output : Refutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 19
% Syntax : Number of formulae : 57 ( 57 unt; 12 def)
% Number of atoms : 57 ( 56 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_comm) ).
fof(f2,axiom,
! [X2,X0,X1] : '+'(X0,'+'(X1,X2)) = '+'('+'(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_assoc) ).
fof(f3,axiom,
! [X0,X1] : times(X0,X1) = times(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_comm) ).
fof(f12,negated_conjecture,
! [X0,X1] : times(s(X0),X1) = '+'(X1,times(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_s) ).
fof(f15,negated_conjecture,
! [X0] : sum(s(X0)) = '+'(s(X0),sum(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_s) ).
fof(f16,negated_conjecture,
'+'(sum(a),sum(a)) = times(a,s(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction_hypothesis) ).
fof(f17,negated_conjecture,
'+'(sum(s(a)),sum(s(a))) != times(s(a),s(s(a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
fof(f32,definition,
! [X0,X1] : sF5(X0,X1) = times(s(X0),X1),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f33,plain,
! [X0,X1] : times(s(X0),X1) = sF5(X0,X1),
inference(reorient_equations,[],[f32]) ).
fof(f34,definition,
! [X0,X1] : sF6(X1,X0) = '+'(X1,times(X0,X1)),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f35,plain,
! [X0,X1] : '+'(X1,times(X0,X1)) = sF6(X1,X0),
inference(reorient_equations,[],[f34]) ).
fof(f36,plain,
! [X0,X1] : sF5(X0,X1) = sF6(X1,X0),
inference(definition_folding,[],[f12,f35,f33]) ).
fof(f40,definition,
! [X0] : sF8(X0) = sum(s(X0)),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f41,plain,
! [X0] : sum(s(X0)) = sF8(X0),
inference(reorient_equations,[],[f40]) ).
fof(f42,definition,
! [X0] : sF9(X0) = '+'(s(X0),sum(X0)),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f43,plain,
! [X0] : '+'(s(X0),sum(X0)) = sF9(X0),
inference(reorient_equations,[],[f42]) ).
fof(f44,plain,
! [X0] : sF8(X0) = sF9(X0),
inference(definition_folding,[],[f15,f43,f41]) ).
fof(f45,definition,
sF10 = sum(a),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f46,plain,
sum(a) = sF10,
inference(reorient_equations,[],[f45]) ).
fof(f47,definition,
sF11 = '+'(sF10,sF10),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f48,plain,
'+'(sF10,sF10) = sF11,
inference(reorient_equations,[],[f47]) ).
fof(f49,definition,
sF12 = s(a),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f50,plain,
s(a) = sF12,
inference(reorient_equations,[],[f49]) ).
fof(f51,definition,
sF13 = times(a,sF12),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f52,plain,
times(a,sF12) = sF13,
inference(reorient_equations,[],[f51]) ).
fof(f53,plain,
sF11 = sF13,
inference(definition_folding,[],[f16,f52,f50,f48,f46,f46]) ).
fof(f54,definition,
sF14 = sum(sF12),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f55,plain,
sum(sF12) = sF14,
inference(reorient_equations,[],[f54]) ).
fof(f56,definition,
sF15 = '+'(sF14,sF14),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f57,plain,
'+'(sF14,sF14) = sF15,
inference(reorient_equations,[],[f56]) ).
fof(f58,definition,
sF16 = s(sF12),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f59,plain,
s(sF12) = sF16,
inference(reorient_equations,[],[f58]) ).
fof(f60,definition,
sF17 = times(sF12,sF16),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f61,plain,
times(sF12,sF16) = sF17,
inference(reorient_equations,[],[f60]) ).
fof(f62,plain,
sF15 != sF17,
inference(definition_folding,[],[f17,f61,f59,f50,f50,f57,f55,f50,f55,f50]) ).
fof(f63,plain,
! [X0] : '+'(s(X0),sum(X0)) = sF8(X0),
inference(forward_demodulation,[],[f44,f43]) ).
fof(f64,plain,
! [X0,X1] : '+'(X1,times(X0,X1)) = sF5(X0,X1),
inference(forward_demodulation,[],[f36,f35]) ).
fof(f69,plain,
! [X0] : sum(s(X0)) = '+'(s(X0),sum(X0)),
inference(forward_demodulation,[],[f63,f41]) ).
fof(f70,plain,
! [X0,X1] : times(s(X0),X1) = '+'(X1,times(X0,X1)),
inference(forward_demodulation,[],[f64,f33]) ).
fof(f146,plain,
sum(sF12) = '+'(sF12,sum(a)),
inference(superposition,[],[f69,f50]) ).
fof(f147,plain,
sum(sF12) = '+'(sF12,sF10),
inference(forward_demodulation,[],[f146,f46]) ).
fof(f149,plain,
sF14 = '+'(sF12,sF10),
inference(forward_demodulation,[],[f147,f55]) ).
fof(f151,plain,
! [X0] : '+'(sF12,'+'(sF10,X0)) = '+'(sF14,X0),
inference(superposition,[],[f2,f149]) ).
fof(f249,plain,
! [X0] : '+'(X0,times(a,X0)) = times(sF12,X0),
inference(superposition,[],[f70,f50]) ).
fof(f251,plain,
! [X0] : '+'(X0,times(sF12,X0)) = times(sF16,X0),
inference(superposition,[],[f70,f59]) ).
fof(f404,plain,
times(sF12,sF12) = '+'(sF12,sF13),
inference(superposition,[],[f249,f52]) ).
fof(f426,plain,
times(sF12,sF12) = '+'(sF12,sF11),
inference(forward_demodulation,[],[f404,f53]) ).
fof(f506,plain,
sF15 = '+'(sF12,'+'(sF10,sF14)),
inference(superposition,[],[f151,f57]) ).
fof(f508,plain,
! [X0] : '+'(sF12,'+'(sF10,X0)) = '+'(X0,sF14),
inference(superposition,[],[f151,f1]) ).
fof(f786,plain,
sF15 = '+'(sF12,'+'(sF12,'+'(sF10,sF10))),
inference(superposition,[],[f506,f508]) ).
fof(f788,plain,
sF15 = '+'(sF12,'+'(sF12,sF11)),
inference(forward_demodulation,[],[f786,f48]) ).
fof(f795,plain,
sF15 = '+'(sF12,times(sF12,sF12)),
inference(forward_demodulation,[],[f788,f426]) ).
fof(f801,plain,
sF15 = times(sF16,sF12),
inference(forward_demodulation,[],[f795,f251]) ).
fof(f806,plain,
sF15 = times(sF12,sF16),
inference(forward_demodulation,[],[f801,f3]) ).
fof(f809,plain,
sF15 = sF17,
inference(forward_demodulation,[],[f806,f61]) ).
fof(f813,plain,
sF15 != sF15,
inference(superposition,[],[f62,f809]) ).
fof(f814,plain,
$false,
inference(trivial_inequality_removal,[],[f813]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUN134-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 22:05:35 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.03/0.88 % (2796524)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.03/0.88 % (2796531)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1603442219:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.03/0.88 % (2796530)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1128377983:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.03/0.88 % (2796533)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2836253283:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.03/0.88 % (2796535)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3003957372:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.03/0.88 % (2796529)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=2120766266:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.03/0.88 % (2796534)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=463680291:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.03/0.88 % (2796532)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1412904994:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.03/0.88 % (2796533)First to succeed.
% 2.03/0.88 % (2796533)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2796524"
% 2.03/0.88 % (2796534)Also succeeded, but the first one will report.
% 2.03/0.88 % (2796532)Instruction limit reached!
% 2.03/0.88 % (2796532)------------------------------
% 2.03/0.88 % (2796532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.03/0.88 % (2796532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.88 % (2796532)CaDiCaL version: 2.1.3
% 2.03/0.88 % (2796532)Termination reason: Instruction limit
% 2.03/0.88 % (2796532)Termination phase: Saturation
% 2.03/0.88 % (2796532)Time elapsed: 0.039 s
% 2.03/0.88 % (2796532)Peak memory usage: 88 MB
% 2.03/0.88 % (2796532)Instructions burned: 138 (million)
% 2.03/0.88 % (2796543)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2598651474:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 2.03/0.88 % (2796533)Refutation found. Thanks to Tanya!
% 2.03/0.88 % SZS status Unsatisfiable for theBenchmark
% 2.03/0.88 % SZS output start Proof for theBenchmark
% See solution above
% 2.03/0.88 % (2796533)------------------------------
% 2.03/0.88 % (2796533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.03/0.88 % (2796533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.88 % (2796533)CaDiCaL version: 2.1.3
% 2.03/0.88 % (2796533)Termination reason: Refutation
% 2.03/0.88 % (2796533)Time elapsed: 0.009 s
% 2.03/0.88 % (2796533)Peak memory usage: 88 MB
% 2.03/0.88 % (2796533)Instructions burned: 25 (million)
% 2.03/0.88 % (2796533)------------------------------
% 2.03/0.88 % (2796533)------------------------------
% 2.03/0.88 % (2796524)Success in time 0.265 s
% 2.03/0.88 % Vampire exiting
%------------------------------------------------------------------------------